Nonadiabatic spin transfer torque in high anisotropy magnetic nanowires with narrow domain walls

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The recent discovery that a spin-polarized current can displace a domain wall (DW) through the spin transfer from conduction electrons to the local magnetization [1] has opened up an alternative approach to manipulate magnetization.Current induced domain wall motion (CIDM) has been investigated experimentally so far in detail in permalloy (Py; Ni 80 Fe 20 ) nanowires characterized by wide DWs (>100 nm) where the spin of a conduction electron is expected to follow adiabatically the magnetization direction as the electron passes across the DW [1,2].A key question that has been raised is whether the spin transfer effect contains nonadiabatic contributions due to spin relaxation or nonadiabatic transport [2][3][4][5][6].It was predicted [3,7] that from the efficiency of the spin transfer effect, which is measured by probing the dependence of the DW propagation magnetic field on the injected current, the nonadiabaticity can be deduced.However, in Py nanowires, the complicated 2D spin structures of the DWs prevent direct comparison to 1D models and a meaningful comparison to full 2D micromagnetic simulations is only possible if the exact spin structure during pulse injection is known, which is generally not the case.In particular, the wall deformations and transformations that have been observed [8] can render the results impossible to interpret in terms of the nonadiabaticity.
To obtain simple DW spin structures, out-of-plane magnetized materials with a strong uniaxial anisotropy can be used where the simple Bloch or Ne ´el DW spin structure is more apt for an analysis using an analytical 1D model including the nonadiabatic torque terms.In addition, a larger nonadiabaticity is expected in these materials due to the larger magnetization gradient for such narrow DWs [2,4,9].This larger nonadiabaticity may explain the high efficiency of the current induced DW depinning reported recently in such materials [10,11].However, another major obstacle for the determination of the nonadiabaticity from the dependence of the DW depinning magnetic field on current is that Joule heating strongly affects the thermally activated DW depinning.For experiments carried out at a constant cryostat temperature, it is thus hard to extract directly the contribution from the spin transfer torque.
In this Letter we probe CIDM in out-of-plane magnetized ðPt=CoÞ 3 =Pt multilayer structures with narrow and simple DWs to deduce the efficiency of the spin transfer torque effect in this material.We find that for conventional measurements, thermal activation effects conceal the real spin torque efficiency and to unambiguously discriminate between spin torque and heating effects, we employ a special measurement scheme, where the sample temperature is kept constant during pulse injection.These measurements yield the real spin torque efficiency and in a detailed analysis we investigate the underlying physical mechanisms for the nonadiabatic spin torque deduced from our measurements.
The Ptð2 nmÞ=½Coð0:6 nmÞ=Ptð1:4 nmÞ 2 =Coð0:6 nmÞ= Ptð2 nmÞ thin film grown on a Si=SiO 2 ð220 nmÞ substrate by sputtering is out-of-plane magnetized as confirmed by polar magneto-optical Kerr effect measurements [see Fig. 1 The effective easy-axis magnetic anisotropy K eff ¼ K u -0 M 2 s =2 was estimated by measuring the dependence of the EHE signal on an hard-axis in-plane applied field.We deduce K eff ¼ 2:7 Â 10 5 J=m 3 at 300 K, in line with other reports [12].Using full 2D micromagnetic simulations [13] (mesh size was 2 Â 2 nm 2 ) and assuming an exchange constant A ¼ 1:6 Â 10 À11 J=m [14], we estimate a DW width Á ¼ ffiffiffiffiffiffiffiffiffiffiffi A=K 0 p % 20 nm (or using the definition ffiffiffiffiffiffiffiffiffiffiffi ffi A=K 0 p % 6:3 nm) with K 0 the effective out-of-plane anisotropy in the wire.Fig. 1(c) (black line) shows an EHE hysteresis cycle for a magnetic field applied perpendicularly to the layer plane.The reversal in steps indicates that the switching occurs through the propagation of a DW successively pinned at different positions inside the cross.The position of the steps varies from one Hall cross to another, which indicates that these steps mainly originate from pinning sites due to natural defects in the film or edge irregularities.
To study the effect of current pulses on the DW depinning, we first pin a DW at a pinning center localized at the entrance of the Hall cross corresponding to the plateau labeled A in Fig. 1(c) by using the magnetic field sequence associated with the red R Hall ðHÞ curve.It should be stressed that this plateau in the EHE can be reproducibly attained over a large temperature range between 4.4 K and room temperature.Starting from zero field, we then increase the magnetic field in steps of 2 Oe.After each step, a current pulse (length 50 s) is injected into the wire [(contacts I À , I þ ), Fig. 1(b)] with a large rise time (18 s).Finally, the Hall resistance is measured.
We present in Fig. 1(c) (blue curve) the resulting R Hall ðHÞ curve for I ¼ À2:5 mA.The injection of the current pulses here leads to a decrease of the depinning field H dep for which a jump from the plateau A in the R Hall ðHÞ curve is observed.In Fig. 2(a) we plot H dep ðjIjÞ for a cryostat temperature of 130 and 250 K for positive and negative currents.For both temperatures, H dep is first approximately constant with jIj for a low current; for a higher current, H dep decreases rapidly with jIj whatever the current polarity although it is higher for positive than for negative currents.As usual, we define the efficiency as the slope j 0 ÁH dep =ÁJj that describes the equivalent effective field felt by the DW due to the presence of current [10,11].For a current distribution approximately uniform across the magnetic film, 1 mA corresponds to a current  216601-2 density J ¼ 2:2 Â 10 11 A=m 2 .This leads to Co=Pt ¼ 9:7 Â 10 À14 Tm 2 =A at 130 K and Co=Pt ¼ 5:9 Â 10 À14 Tm 2 =A at 250 K for negative current, about 1 order of magnitude higher than the one deduced by a similar method in permalloy nanowires [15] ( Py % 5 Â 10 À15 Tm 2 =A).
Figure 2(a) suggests that two distinct effects are involved in the DW depinning: a first effect that is independent of the current polarity, likely to be due to Joule heating and a second one that depends on the sign of the current.To clarify this point and separate both contributions, we employ a special experimental scheme to carry out all the following measurements at a constant temperature of the sample.First, the sample temperature is determined by using the four-point resistance of the wire during current injection as a thermometer [16] with the same method as described in Refs.[15].As an example, the resistance and corresponding temperature rise ÁT is shown in the inset of Fig. 2(a) as a function of I for a cryostat temperature of T cryo ¼ 130 K.The temperature increases approximately quadratically with I and can reach values up to 200 K for the maximum injected current.This information is then used to adjust the injected current so that for each cryostat temperature the sample temperature is constant.
We present in Fig. 2(b) H dep ðIÞ for a constant sample temperature T sample ¼ 250 K (up triangles) and T sample ¼ 300 K (down triangles).We start with T sample ¼ 250 K, where the behavior is very different from the one observed for a constant cryostat temperature: H dep decreases with jIj for a negative current (H À dep ðIÞ) but not for a positive current (H þ dep ðIÞ), where it shows only little change with jIj and H þ dep ðIÞ > H À dep ðIÞ.Current thus makes the depinning easier only for one current polarity.The dependence of H dep on jIj for negative current as well as the different behavior for both current polarities clearly demonstrate that this effect is not due to Joule heating.A real efficiency % 2:5 Â 10 À14 Tm 2 =A results, that is smaller than the one that can be deduced for a constant cryostat temperature at 250 K.If we compare this value to the one deduced from the T cryo ¼ 130 K H dep ðjIjÞ curve for I ¼ 2:25 mA corresponding to T sample ¼ 250 K, we see that the Joule heating contributes to about 75% of the depinning efficiency measured with the conventional approach at a constant cryostat temperature.Thus Joule heating plays here an important role in the DW depinning and it is clear that measurements at a constant cryostat temperature do not allow one to determine the pure effect of the spin transfer torque.The H dep ðIÞ curve at T sample ¼ 300 K is qualitatively similar to the one obtained at T sample ¼ 250 K although the dependence of H dep on jIj is much weaker for negative current with % 6:0 Â 10 À15 Tm 2 =A.
Several mechanisms may lead to the current polarity dependent variation of the depinning field for the constant sample temperature experiment.First, we consider the DW drag [18,19] creating a perpendicular magnetic field B z / tanð h ÞJ, with h the Hall angle.Using the expression of B z proposed by Viret et al. [19], and tan h % 0:025 measured experimentally, we obtain an efficiency ¼ B z =J % 2:3 Â 10 À16 Tm 2 =A, i.e., at least 1 order of magnitude smaller than the one we measure at T sample equal to 250 K or 300 K. Therefore this effect cannot explain our observation.Second, the Oersted field generated by the current might a play a role, but the resultant force on the DW is zero, and so this effect should be negligible.Furthermore, the Oersted field should be the same for T sample equal to 250 K or 300 K and therefore it cannot explain the decrease of the efficiency for increasing T sample .
Third, we consider the adiabatic spin transfer torque proposed by Berger [1] and more recently by Tatara et al. [2].We note first that our experiments correspond to the low pinning case discussed by Tatara et al. [2] expected if H pin < H k =, with H pin pinning field, H k the hard-axis anisotropy field and the Gilbert damping.Indeed, we estimate H pin $ 470 Oe from the H dep ðTÞ curves much smaller than H k = % 5000 Oe with $ 0:15 in our films [20,21] and 0 H k % 0:075 T for our 530 nm wide wire deduced from hard-axis magnetometry combined with 2D micromagnetic simulations [13].In addition, for our quasistatic 18 s pulse rise time, we do not expect any subthreshold dynamical depinning [1,22].Thus, depinning should only occur at the critical current density J c for steady motion associated with the ''intrinsic pinning'' due to the DW demagnetizing energy [2].In the rigid DW approximation [3], J c ¼ eM s 0 H k ðA=ðK 0 þ K=2ÞÞ 1=2 =ð@PÞ, with P the polarization of the current, and K ¼ 0 M s H k =2.For P ¼ 0:46 in Co, we obtain J c ¼ 2:1 Â 10 12 A=m 2 much higher than the lowest current density for which CIDM was observed (J % 4 Â 10 11 A=m 2 ).Moreover, the strong decrease of H dep with jIj for negative current is not compatible with a purely adiabatic spin torque.Indeed, J c should not depend on H in the adiabatic case at all for our quasistatic current pulse (as also predicted by numerical simulations) since H does not change the demagnetizing energy of the pinned DW, that controls the current induced depinning under this assumption [23].We therefore conclude that the adiabatic spin transfer torque cannot account for our experimental results.
Thus, what remains as a possible explanation are torque terms beyond the adiabatic term: the torque due to the spin relaxation in the wall described by the dimensionless parameter SR [3,5] and the torque due to a higher order nonadiabatic correction whose effect is equivalent to a momentum transfer from the conduction electron to the DW (parameter NA ) [2,6].These torques exert a force on the wall similar to the effect of an effective perpendicular magnetic field B with B=J ¼ ¼ P@=ð2eM s ÁÞ with ¼ SR þ NA .Such a behavior is in qualitative agreement with the linear variation of the depinning field with current I.
From the efficiency derived in our experiment for negative current at constant sample temperature, we obtain 216601-3 % 1:45 at 250 K and % 0:35 at 300 K.For the spin relaxation mechanism, several theoretical approaches [6] predict SR to be of the order of the damping parameter , which is about 0.15 in our films [20,21].These values are significantly lower than the we deduced experimentally [24].So a possible remaining effect is the momentum transfer mechanism.The parameter NA in the ballistic limit is a function of the domain wall resistance [2] R DW with NA ¼ e 2 nAR DW Á=P@ ¼ e 2 n DW Á 2 =P@ with n the electron density, A the lateral cross section of the wire, DW ¼ R DW A=Á the DW resistivity.For n ¼ 5:6 Â 10 28 m À3 in Co [25], a DW resistivity DW ¼ 3:9 Â 10 À10 m can be derived from the T sample ¼ 250 K value ( DW ¼ 0:9 Â 10 À10 m for T sample ¼ 300 K) that agrees with the DW resistivity measured by Aziz et al. [26] in similar Ptð3:5 nmÞ=Coð0:6 nmÞ=Ptð1:6 nmÞ structures at room temperature ( DW ¼ 2:3 Â 10 À10 m).The momentum transfer is thus a possible mechanism to explain our experimental results.We note, however, that momentum transfer due to nonadiabaticity is predicted [4,6,27] to be small for our DWs with widths that are large compared to the Fermi wavelength and larger than the Larmor precession length [4,6] or the mean free path [27] and this calls for further theoretical works [28].
It should also be noted that the nonadiabatic spin torque effect term predicts a symmetric behavior with the current polarity; i.e., the decrease in the depinning field for a negative current should be equal to the increase for a positive current.We see in Fig. 2(b) that we do not observe a completely symmetric behavior.In particular, the distribution of the depinning field, marked by the error bars in Fig. 2(b) is always smaller for negative currents, where current helps to depin the DW, than for positive currents and this behavior is observed consistently but is presently not well understood.Furthermore only a clear decrease of H dep is observed for negative current.This suggests that an additional effect is involved in the current induced depinning process that seems to help the DW depinning whatever the current polarity.
Finally, the models invoked so far do not explain the strong decrease of the efficiency observed as the sample temperature increase from 250 to 300 K since we expect little variation of Á, M s , DW [30] or spin relaxation rate in this small temperature range.For Py, Laufenberg et al. [15] observed a corresponding increase of the zero field critical current with sample temperature.This can be attributed to the onset of thermally activated spin waves that effectively carry away angular momentum [31], which may explain the observed reduction of the efficiency with increasing temperature in our case.
In conclusion, we have used a special measurement scheme to investigate spin transfer in high anisotropy out-of-plane magnetized (Pt=Co) multilayer elements with narrow domain walls.We determine the real efficiency of the spin transfer torque effect from measurements of the depinning field as a function of the current pulse amplitude at a constant sample temperature.This has not been possible previously using conventional measurements at a constant cryostat temperature where, as we directly demonstrate, thermal activation effects dominate.From the real efficiency, the nonadiabaticity of the spin transfer is determined in this material and we find that our observations are consistent with a momentum transfer mechanism.
The authors thank G.
(a)].SQUID magnetometry reveals a saturation magnetization of the film M s ¼ 1:4 Â 10 6 A=m at 300 K. 530 nm wide wires [Fig.1(b)] along which three 530 Â 530 nm 2 Hall crosses were fabricated by e-beam lithography and lift-off [Fig.1(b), inset].A 200 nm AlN insulating capping layer with high thermal conductivity was then deposited by sputtering.The position of the DW is detected with high sensitivity in a Hall cross [Fig.1(b), contacts V À V þ ] by the extraordinary Hall effect (EHE).The Hall voltage is measured using a standard lock-in technique with a small ac current (2 A) [Fig.1(b), contacts

FIG. 2 (
FIG. 2 (color online).(a) (b) H dep as a function of jIj for (a) a constant cryostat temperature of T cryo ¼ 130 K (squares) and T cryo ¼ 250 K (circles) and (b) a constant sample temperature of T sample ¼ 250 K (up triangles) and T sample ¼ 300 K (down tri angles).Each point corresponds to the mean value of H dep aver aged over 10 measurements or more and the error bars show the standard deviation.In (b), the black lines are a linear fit of the data.Inset in (a): dependence of the resistance and of the sample temperature rise ÁT with the current for T cryo ¼ 130 K.

FIG. 1 (
FIG.1(color online).(a) Polar Kerr rotation angle as a func tion of the magnetic field applied perpendicular to the film plane of the unpatterned Pt=ðCo=PtÞ 3 film at room temperature.(b) SEM image of the structure; inset: SEM image of the Hall cross connected to the gold electrodes.(c) Hall resistance vs the perpendicular applied magnetic field at T cryo ¼ 180 K; the black curve (full squares) corresponds to a full hysteresis cycle, the red curve (down triangles) was measured while preparing the mag netic state to plateau A. For the blue curve (up triangles), current pulses of 2:5 mA were injected before measuring the Hall resistance.H dep is indicated for the black curve.
Tatara and M. Stiles for useful discussions and acknowledge support by the Samsung Advanced Institute of Technology, the DFG (SFB513 and SFB767) and the EU (ERC-2007-StG208162 and SPINSWITCH MRTN-CT-2006-035327).